EROSION BY PLANAR TURBULENT WALL JETS

New scaling laws are presented for the spatial variation of the mean v elocity and lateral extent of a two-dimensional turbulent wall jet, fl owing over a fixed rough boundary. These scalings are analogous to tho se derived by Wygnanski et nl. (1992) for the flow of a wall jet over a smooth boundary. They reveal that the characteristics of the jet dep end weakly upon the roughness length associated with the boundary, as confirmed by experimental studies (Rajaratnam 1967). These laws are us ed in the development of an analytical framework to model the progress ive erosion of an initially flat bed of grains by a turbulent jet. The grains are eroded if the shear stress, exerted on the grains at the s urface of the bed, exceeds a critical value which is a function of the physical characteristics of the grains. After the walljet has been fl owing for a sufficiently long period, the boundary attains a steady st ate, in which the mobilizing forces associated with the jet are insuff icient to further erode the boundary. The steady-state profile is calc ulated separately by applying critical conditions along the bed surfac e for the incipient motion of particles. These conditions invoke a rel ationship between the mobilizing force exerted by the jet, the weight of the particles and the local gradient of the bed. Use of the new sca ling laws for the downstream variation of the boundary shear stress th en permits the calculation of the shape of the steady-state scour pit. The predicted profiles are in good agreement with the experimental st udies on the erosive action of submerged water and air jets on beds of sand and polystryene particles (Rajaratnam 1981). The shape of the er oded boundary at intermediate times, before the steady state is attain ed, is elucidated by the application of a sediment-volume conservation equation. This relationship balances the rate of change of the bed el evation with the divergence of the flux of particles in motion. The fl ux of particles in motion is given by a semiempirical function of the amount by which the boundary shear stress exceeds that required for in cipient motion. Hence the conservation equation may be integrated to r eveal the transient profiles of the eroded bed. There is good agreemen t between these calculated profiles and experimental observations (Raj aratnam 1981).